VA group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots?

0.76%

Step-by-step explanation:

This exercise is solved through combinations.

The first is the number of combinations of students that would go in that course, that is, 5 out of 40.

Formula: nCx = n! / X! * (N-x)!

 40C5 = 40! / [5! * (40 - 5)!] = 658008

Also the number of combinations of the other members of the audience that occupy the other 4 places (9 in total - 5 of the group), that is 4 of 90 (130 total - 40 of the group658008po).

90C4 = 90! / [4! * (90 - 4)!] = 2555190

The total of possible combinations 9 contestants with 5 students in them, would be:

40C5 * 90C4

Now, the total number of possible 9 contestants from the audience would be 9 in 130:

130C9 = 130! / [9! * (130 - 9)! = 2.2016 * 10 ^ 13

The probability would be equal to:

40C5 * 90C4 / 130C9 = 658008 * 2555190 / (2.2016 * 10 ^ 13) = 0.076

In other words, the probability is 0.76%

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b